Sovereign Risk, Fiscal Policy, and Macroeconomic …Sovereign Risk, Fiscal Policy, and Macroeconomic Stability Prepared by Giancarlo Corsetti, Keith Kuester, Andre Meier, and Gernot

Sovereign Risk, Fiscal Policy, and Macroeconomic Stability

Giancarlo Corsetti, Keith Kuester, Andre Meier, and Gernot J. Mueller

WP/12/33

© 2012 International Monetary Fund WP/12/33

IMF Working Paper

Monetary and Capital Markets Department

Sovereign Risk, Fiscal Policy, and Macroeconomic Stability

Prepared by Giancarlo Corsetti, Keith Kuester, Andre Meier, and Gernot J. Mueller1

Authorized for distribution by Peter Dattels

January 2012

Abstract

This paper analyzes the impact of strained government finances on macroeconomic stability and the transmission of fiscal policy. Using a variant of the model by Curdia and Woodford (2009), we study a “sovereign risk channel” through which sovereign default risk raises funding costs in the private sector. If monetary policy is constrained, the sovereign risk channel exacerbates indeterminacy problems: private-sector beliefs of a weakening economy may become self-fulfilling. In addition, sovereign risk amplifies the effects of negative cyclical shocks. Under those conditions, fiscal retrenchment can help curtail the risk of macroeconomic instability and, in extreme cases, even stimulate economic activity.

JEL Classification Numbers: E32, E52, E62

Keywords: Fiscal policy, monetary policy, zero lower bound, risk premium, sovereign risk

Author’s E-Mail: [email protected], [email protected], [email protected], and [email protected]

1 Corsetti: Cambridge University and CEPR, Kuester: Federal Reserve Bank of Philadelphia, Meier: IMF, Mueller: University of Bonn and CEPR. An earlier draft of this paper was circulated under the title “Sovereign risk and the effects of fiscal retrenchment in deep recessions.” For very helpful comments, we thank Santiago Acosta-Ormaechea, John Bluedorn, Fabian Bornhorst, Hafedh Bouakez, Antonio Fatas, Philip Lane, Thomas Laubach, Daniel Leigh, Ludger Schuknecht, and the participants in seminars at the Board of Governors, Bundesbank-Banque de France, Goethe University, IMF, Midwest Macro Meetings, Society for Computational Economics, and Sveriges Riksbank. Corsetti’s work on this paper is part of PEGGED, Contract no. SSH7-CT-2008-217559 within the 7th Framework Programme for Research and Technological Development. Support from the Pierre Werner Chair Programme at the EUI is gratefully acknowledged. The views expressed herein are those of the authors and do not necessarily represent those of the Federal Reserve Bank of Philadelphia or the Federal Reserve System.

This Working Paper should not be reported as representing the views of the IMF. The views expressed in this Working Paper are those of the author(s) and do not necessarily represent those of the IMF or IMF policy. Working Papers describe research in progress by the author(s) and are published to elicit comments and to further debate.

1 Introduction

In the wake of the global financial crisis, sovereign risk premia have risen sharply in several

countries, prompting policymakers to start fiscal tightening even as private demand remains

weak. What are the likely consequences for economic activity? The present paper assesses

this question quantitatively, starting from the observation that sovereign funding strains tend

to spill over into private credit markets.1 Through this sovereign risk channel, higher public

indebtedness may adversely affect economic activity by raising private-sector financing costs.

Conversely, upfront fiscal retrenchment may help improve credit conditions in the broader

economy, thereby counteracting the direct contractionary effect of lower public spending.

Recent developments in Europe provide clear evidence in support of spillovers from sovereign

risk to broader financial conditions. The panels in Figure 1 display time-series data on credit

default swap (CDS) spreads for government debt and nonfinancial corporate debt.2 The

figure compares two sets of euro area countries: those with relatively low sovereign spreads

(left panel) and those with relatively high sovereign spreads (Belgium, Greece, Ireland, Italy,

Portugal, and Spain).3 The series display substantial comovement, particularly in countries

that face fiscal strain (right panel). For the time period shown, the daily correlation between

corporate and sovereign CDS spreads in high-spread countries is 0.71. For the low-spread

countries, it is lower, but still significantly positive at 0.36 percent.

In this paper, we formally explore the implications of the sovereign risk channel. We build on

the model proposed by Curdia and Woodford (2009), in which heterogeneous households en-

gage in borrowing and lending via financial intermediaries. Our variant of the model features

two critical innovations. First, we allow for sovereign risk premia that respond to changes in

the fiscal outlook of the country. Although the precise numerical relationship is uncertain and

1This is prominently embedded in the notion of a “sovereign ceiling.” In a strict interpretation, the sovereignceiling posits that no debtor in a given country can have a better credit quality than the government, a primaryreason being the state’s capacity to extract private-sector resources through taxation. In reality, severalauthors, including Durbin and Ng (2005), have documented exceptions to this rule, notably for firms withsubstantial export earnings or foreign operations. Even then, however, sovereign and corporate bond yieldstend to comove significantly (see the literature review in Cavallo and Valenzuela (2007) or Harjes (2011)). Inthe context of the global financial crisis, both the International Monetary Fund (2010a) and the EuropeanCentral Bank (2010) have stressed that government bond yields typically have a strong influence on domesticcorporate bond yields.

2A similar set of charts was first provided in International Monetary Fund (2011).3We focus here on evidence for the euro area in order to control for the impact of monetary policy. Indeed,

monetary policy is a key factor in determining the strength of the sovereign risk channel according to ouranalysis below.

2

Figure 1: Sovereign and nonfinancial corporate CDS spreads

150

200

250

300

350

Nonfinancial corporates

Sovereigns

CDS Spreads in Low!Spread Euro Area

(Basis points)

0

50

100

150

200

250

300

350

2008 2009 2010 2011


Sovereigns

CDS Spreads in Low!Spread Euro Area

(Basis points)

200

250

300

350

400

450


Sovereigns

CDS Spreads in High!Spread Euro Area

(Basis points)

0

50

100

150

200

250

300

350

400

450

2008 2009 2010 2011


Sovereigns

CDS Spreads in High!Spread Euro Area

(Basis points)

Notes: 5-year CDS spreads in low-spread and high-spread euro area countries, as well as for nonfinancialcorporations headquartered there. Low-spread euro area includes Austria (number of firms in our sample: 1),Finland (1), France (24), Germany (18), and Netherlands (8). High-spread euro area includes Belgium (numberof firms: 1), Greece (1), Ireland (0), Italy (4), Portugal (2), and Spain (4). The corporations in our sampleare the constituents of the Itraxx Europe index. The same relative weights are adopted for the sovereign andcorporate index series. For example, of the 52 firms in the low-spread euro area sample, 24 are headquarteredin France. As a result, in the sovereign low-spread euro area series, France has a weight of 24/52. Data sources:Bloomberg; Markit.

likely to vary over time, the basic premise that risk premia are affected by fundamentals should

be uncontroversial. Second, private credit spreads rise with sovereign risk because strained

public finances raise the cost of financial intermediation. This way of modeling spillovers

allows for a tractable representation of the sovereign risk channel within a simple variant of

the canonical New Keynesian model. Consequently, we are in a position to supplement our

numerical results with analytical solutions for interesting special cases.

The sovereign risk channel amplifies the transmission of shocks to aggregate demand, unless

monetary policy manages to offset the spillover from sovereign default risk to private funding

costs. Offsetting higher sovereign risk premia would typically require cuts in the policy rate.

However, the central bank’s capacity to enact such cuts may be hampered, most notably if

the nominal interest rate is already at the zero lower bound (ZLB), as has been the case for

several major central banks in recent years. Our model is developed with an explicit reference

to this ZLB problem. Yet it is important to stress that the ZLB is but one prominent example

of a constraint on central bank action. Monetary policy would be similarly constrained—and

our analysis would carry through—under a currency peg or in other situations where political

or institutional considerations prevent the central bank from counteracting a rise in sovereign

risk premia.

3

Our analysis of the sovereign risk channel gives rise to two distinct sets of results for an en-

vironment where monetary policy is constrained. First, under these circumstances sovereign

risk may give rise to indeterminacy, or belief-driven equilibria. Specifically, to the extent that

a pessimistic shift in expectations (unrelated to fundamentals) implies an upward revision

of the projected government deficit, the risk premium on public debt rises and, through the

sovereign risk channel, spills over to private borrowing costs. Higher private funding costs, in

turn, slow down activity, validating the initial adverse shift in expectations. Under normal

circumstances, this scenario could be averted by the central bank’s commitment to appro-

priately lower the policy rate. To the extent that monetary policy is constrained, however,

expectations may become self-fulfilling, especially when sovereign risk is very high. In this

scenario, we also find that the anticipation of a procyclical spending response—that is, fiscal

tightening in response to a cyclical fall in tax revenue—can help to ensure determinacy.

Our second set of results suggests that (under equilibrium determinacy) the sign and the size

of the government spending multiplier depend critically on the state of the economy. When

the central bank is unconstrained, the sovereign risk channel is not operative in our model,

as looser monetary policy can offset the impact of higher risk premia. By contrast, when

the central bank is constrained, the sovereign risk channel typically reduces the spending

multiplier. Fiscal retrenchment, by improving the outlook for public finances, may thus

have less adverse effects on economic activity relative to a situation where sovereign risk

is absent. These departures from standard macroeconomic results remain fairly modest as

long as sovereign risk is contained. Only when public finances are very fragile, sovereign risk

is high, and monetary policy is constrained for an extended period, does the sovereign risk

channel unfold a sizeable impact on economic outcomes. The more severe the prevailing strain

on public finances, the less fiscal retrenchment will weigh on growth. In relatively extreme

cases, tighter fiscal policy may even stimulate economic activity.

As a caveat we emphasize that the present paper is not meant to add to the theory of

sovereign default. Following Eaton and Gersovitz (1981), a number of authors, including

Arellano (2008) and Mendoza and Yue (2010), have recently modeled default as a strategic

decision of a sovereign that balances the gains from foregone debt service against the costs of

exclusion from international credit markets. In equilibrium this implies that the probability

of default increases in the level of debt. In order to maintain the tractability of our model for

4

business cycle analysis, we impose such a relationship without explicitly modeling a strategic

default decision. Specifically, we link the sovereign risk premium to the expected path of

public debt (or, alternatively, future fiscal deficits). We thereby abstract from a number of

other factors that may also affect the market’s assessment of sovereign risk, such as the quality

of fiscal institutions or the composition of the investor base for government bonds. Implicit

in our approach to modeling sovereign risk is the assumption that there are limits to credible

commitment on the part of fiscal policymakers; otherwise, there would be no risk premium

in the first place, and policymakers seeking to protect growth would arguably prefer to delay

retrenchment until the economy is on a firm recovery path.

The remainder of the paper is structured as follows. Section 2 describes the model economy

and presents our calibration. Sections 3 and 4 report analytical results and results from model

simulations, respectively. Section 5 concludes.

2 The model

The key motivation for our model is the observation that sovereign risk systematically affects

private-sector borrowing conditions. The model, therefore, needs to account for the possibility

that private-sector borrowing and lending take place in equilibrium. We rely on the framework

developed by Curdia and Woodford (2009) (CW, henceforth), which gives rise to an interest

rate spread in an otherwise standard New Keynesian model. The spread emerges as a result of

heterogeneity among households and because of costly financial intermediation. By assuming

asymptotic risk sharing, CW are able to maintain the tractability of the New Keynesian

baseline model. We add to their model a slightly richer specification of fiscal policy and allow

the state of public finances to affect financial intermediation. In the following we briefly outline

the model and stress the instances in which we depart from the original CW formulation.

2.1 Households

The economy is populated by a unit measure of households indexed by i ∈ [0, 1]. Household

i is of one of two types, indexed by superscript τ t(i) ∈ b, s. In equilibrium, households of

type τ t(i) = b will be “borrowers,” and households of type s will be “savers.” Households

infrequently change their type. In each period, the probability of redrawing a type is 1 − δ,

5

where δ ∈ (0, 1). Conditional on redrawing, the household will end up being a borrower with

probability πb, and a saver with probability πs = 1−πb. The objective of household i ∈ [0, 1]

is given by

E0

∞∑

t=0

(etβt)

[(ξτ )σ

−1τ [ct(i)]

1−σ−1τ

1− σ−1τ

−ψτ

1 + νht(i)

1+ν

],

where ct(i) is an aggregate of household expenditures:

ct(i) =

[∫ 1

0ct(j, i)

θ−1θ dj

] θθ−1

; θ > 1. (1)

Here ct(j, i) is a differentiated output good produced by firm j ∈ [0, 1]. ht(i) denotes hours

worked by the household. et is a unit-mean shock to the time-discount factor β ∈ (0, 1), and

ξτ , στ , ψτ , and ν are positive parameters.

Households are able to insure against idiosyncratic risk through state-contingent contracts.

Yet the resulting transfer payments are assumed to occur infrequently, namely only in those

periods in which a household is assigned a new type. Meanwhile, households may borrow or

save through financial intermediaries. The beginning-of-period wealth of household i is given

by

At(i) = [Bt−1(i)]+(1+idt−1)+[Bt−1(i)]

−(1+ibt−1)+(1−ϑt)Bgt−1(i)(1+i

gt−1)+D

intt +Tt(i)+T

ct .

(2)

Here [Bt−1(i)]+ denotes deposits at financial intermediaries at the end of the previous period,

which earn the deposit rate idt−1; [Bt−1(i)]− denotes debt at financial intermediaries, which

charge the borrowing rate ibt−1. In equilibrium, household i is either borrowing or saving. In

the case where it is saving, the household may also hold government debt Bgt−1(i) ≥ 0.

We depart from CW by assuming that government debt is not riskless: in any period, the

government may honor its debt obligations, in which case ϑt = 0; or it may partially default,

in which case ϑt = ϑdef, with ϑdef ∈ [0, 1) indicating the size of the haircut. igt−1 is the notional

interest rate on government debt. Dintt are profits from competitive financial intermediaries

that are distributed across households in a lump-summanner. Tt(i) denotes transfers resulting

from state-contingent contracts (which are zero for those households that do not redraw their

type and are therefore temporarily without access to the payoff scheme implied by asymptotic

risk sharing). T ct is a lump-sum transfer that, in case of a sovereign default, compensates bond

6

holders for losses associated with the sovereign default. Yet the payment is not proportional

to the size of an individual’s holdings of government debt (see Schabert and van Wijnbergen

(2008) for a similar setup). This assumption, along with the risk of a haircut, drives a wedge

between the risk-free rate, idt , and the interest rate on government debt, igt .

The end-of-period wealth of household i is given by

Bt(i) = At(i)− Ptct(i) + (1− τwt )Ptwtht(i) +Dt − T gt . (3)

Pt denotes the consumption price index, τwt is the labor tax rate, and wt is the economy-wide

real wage rate; Dt are profits earned by intermediary goods producers and −T gt are lump-sum

transfers by the government.

Assuming identical initial wealth for all households, state-contingent contracts ensure that

post-transfer wealth is identical for all households that are selected to redraw their type. It

is given by

At = [dt−1(1 + idt−1) + (1− ϑt)bgt−1(1 + igt−1)− bt−1(1 + ibt−1)]Pt−1 +Dint

t + T ct , (4)

where bgt denotes government debt in real terms. dt denotes aggregate savings deposited with

intermediaries, and bt denotes aggregate private borrowing, both in real terms. The latter

evolves according to

bt = δbt−1(1 + ωt−1)(1 + idt−1)/Πt − πbωtbt + πb[δbgt−1(1 + igt−1)/Πt − bgt

](5)

+πbπs[(cbt − cst )− (1− τwt )(wth

bt −wth

st )].

Intuitively, the accumulation of debt depends on four terms. The first term is the last pe-

riod’s private debt level plus interest (for those households that do not redraw their type).

The second term, -πbωtbt, is the gain accruing to borrowing households from fraudulent loans

(discussed below). The third term captures whether sovereign indebtedness (suitably ad-

justed for the change in household types) falls. In order to reduce sovereign indebtedness,

current taxes need to be relatively high, which increases the need for borrowing by borrowers.

Put differently, if sovereign indebtedness falls, so that[δbgt−1(1 + igt−1)/Πt − bgt

]> 0, more re-

sources are made available by savers to borrowers since savers resort more to private sources

7

for storing value. The last term captures the difference in consumption levels relative to the

difference in wage income across household types.

Turning to the intertemporal consumption decisions, note that, as a result of asymptotic risk

sharing, all households of a specific type have a common marginal utility of real income, λτt ,

and choose the same level of expenditure:

cst = ξs(λst)−σs (6)

cbt = ξb(λbt)−σb . (7)

The optimal choices regarding borrowing from and lending to intermediaries, as well as to

the government, are then governed by the following Euler equations:

etλst = βEt

[et+1

1 + idtΠt+1

(1− δ)πbλ

bt+1 + [δ + (1− δ)πs]λ

st+1

], (8)

etλst = βEt

[et+1

(1− ϑt+1)(1 + igt )

Πt+1

(1− δ)πbλ

bt+1 + [δ + (1− δ)πs]λ

st+1

], (9)

etλbt = βEt

[et+1

1 + ibtΠt+1

(1− δ)πsλ

st+1 + [δ + (1− δ)πb]λ

bt+1

]. (10)

Optimal labor supply by households, in turn, is given by

hst =

(λstψs

(1− τwt )wt

)1/ν

, (11)

hbt =

(λbtψb

(1− τwt )wt

)1/ν

. (12)

Across household types, average labor supply, ht = πbhbt + (1− πb)h

st , is given by

ht =

(Λtψ(1− τwt )wt

)1/ν

, (13)

where

Λt := ψ

πb

(λbtψb

)1/ν

+ πs

(λstψs

)1/νν

(14)

8

and ψ−1/ν = πbψ−1/νb + πsψ

−1/νs . Finally, for future reference we define

λt = πbλbt + (1− πb)λ

st (15)

as the average marginal utility of real income across types.

2.2 Financial intermediaries

Saving and borrowing across households of different types takes place through perfectly com-

petitive financial intermediaries. As in CW, we assume that an interest rate spread emerges

because financial intermediation requires resources, Ξtbt, and because in each period a frac-

tion of loans, χt, cannot be recovered, irrespective of the characteristics of borrowers (due

to, say, fraud). Moreover, deposits, dt, are assumed to be riskless and intermediaries collect

the largest quantity of deposits that can be repaid from the proceeds of the loans that they

originate, that is, (1+ idt )dt = (1+ ibt)bt. The cash flow in period t of a financial intermediary

is thus given by dt−bt−χtbt−Ξtbt. Using ωt to define the spread between lending and deposit

rates, we have

1 + ωt =1 + ibt1 + idt

. (16)

Substituting dt = (1 + ωt)bt, and choosing bt to maximize the profits of the intermediary

yields the first-order condition for loan origination

ωt = χt + Ξt. (17)

In departing from CW, we assume that either χt or Ξt depends on sovereign risk. This

assumption captures the increased difficulties in monitoring and enforcing loan contracts in

an economy under fiscal strain. Conceptually related is the notion that in case of a sovereign

default, the government diverts funds from the repayments made by borrowers, see Mendoza

and Yue (2010).

Costs χtbt and Ξtbt differ in that only the latter are assumed to enter the economy’s resource

constraint. For the linearized version of the model, used in Section 3, we let loan origination

costs be covered by χt > 0, and set Ξt = 0, which facilitates deriving analytical results. For

the dynamic simulations in Section 4 we set χt = 0 and let Ξt > 0. Specifically, we assume

9

that either

χt = χψ[(1 + igt )/(1 + idt )]αψ − 1 and Ξt = 0, (18)

or

χt = 0 and Ξt = χψ[(1 + igt )/(1 + idt )]αψ − 1, (19)

where parameter χψ > 0 is used to scale the private spread in the steady state, and αψ

measures the strength of the spillover from the (log) sovereign risk premium to the (log)

private risk premium. Finally, transfers from intermediaries to households include loans that

are not recovered by the intermediaries such that Dintt = Pt(ωtbt − Ξt bt).

2.3 Firms

There is a continuum of firms j ∈ [0, 1], each of which produces a differentiated good on the

basis of the following technology

yt(j) = zth(j)1/φ, (20)

where zt is an aggregate productivity shock. In each period only a fraction (1−α) of firms is

able to reoptimize its prices. Firms that do not reoptimize adjust their price by the steady-

state rate of inflation, Π. Prices are set in period t to maximize expected discounted future

profits.4 The resulting first-order condition for a generic firm that adjusts its price, P ∗

t , is

(P ∗

t

Pt

)1+θ(φ−1)

=Kt

Ft, (21)

with

Kt = λtetµpφwt

(ytzt

)φ+ αβEt

[(Πt+1

Π

)θφKt+1

], (22)

Ft = λtetyt + αβEt

[(Πt+1

Π

)(θ−1)

Ft+1

], (23)

4Future nominal profits are discounted with the factor (αβ)T−t λT

λt

Pt

PT, taking into account that demand for

product j is given by the demand function yt(j) = yt(Pt(j)/Pt)−θ, where Pt(j) denotes the price of good j,

and yt is aggregate output.

10

where µp = θ/(θ − 1). The law of motion for prices (inflation) is given by

1− α

(ΠtΠ

)θ−1

= (1− α)

(P ∗

t

Pt

)1−θ

. (24)

For future reference it is also useful to define price dispersion ∆t :=∫ 10

(Pj,tPt

)−θφ

dj, which

evolves as follows

∆t = α∆t−1

(ΠtΠ

)θφ+ (1− α)

(1− α (Πt/Π)

θ−1

1− α

) θφθ−1

. (25)

Finally, profits distributed to households are given by Dt =∫ 10 Pt(j)yt(j) − Ptwtht(j)dj; or,

in equilibrium, Dt = Pt

(yt − wt (yt/zt)

φ∆t

).

2.4 Government

Real government debt evolves as follows:

bgt = (1− ϑt)bgt−1(1 + igt−1)

Πt+ gt +

T ctPt

−T gtPt

− τwt wtht,

where gt denotes government spending. Below we will consider different assumptions regard-

ing the law of motion for government spending. As is customary, we assume throughout that

the expenditure share of each particular differentiated good in government spending is the

same as the share of that good in private consumption. By assumption, transfers T ct ensure

that a sovereign default is neutral ex post in regard to any distributional consequences and

the debt level. That is, under our assumptions, a sovereign default does not automatically

ease the degree of fiscal strain. In particular, we set

T ct = Ptϑtbgt−1(1 + igt−1)

Πt.

The consolidated government flow budget constraint is thus given by

bgt =bgt−1(1 + igt−1)

Πt+ gt −

T gtPt

− τwt wtht. (26)

11

Letting

trt = τwt wtht + T gt /Pt (27)

denote the part of taxes that is related to the business cycle and to stabilization policy, we

assume

(trt − t) =[φT,y(yt − y) + φT,bg(b

gt−1 − bg)

], φT,y ≥ 0, φT,bg > 0. (28)

Throughout the paper, we assume that φT,bg is large enough so as to eventually stabilize

public debt.5

While actual default is neutral in the sense described above, the probability of default is

crucial for the pricing of government debt, (igt ), and for real activity.6 A fully specified model

of sovereign default is beyond the scope of the present paper. Instead, we draw on earlier

work in this area, which has pursued two distinct approaches. First, following Eaton and

Gersovitz (1981), Arellano (2008) and others have modeled default as a strategic decision of

the sovereign. Second, and more recently, Bi and Leeper (2010) and Juessen et al. (2011)

consider default as the consequence of the government’s inability to raise the funds necessary

to honor its debt obligations. Under both approaches, the probability of sovereign default is

closely and nonlinearly linked to the level of public debt.

In the current paper we operationalize sovereign default by appealing to the notion of a fiscal

limit in a manner similar to Bi and Leeper (2010). Whenever the debt level rises above the

fiscal limit, default will occur. The fiscal limit is determined stochastically, capturing the un-

certainty that surrounds the political process in the context of sovereign default. Specifically,

we assume that in each period the limit will be drawn from a generalized beta distribution

with parameters αbg , βbg , and bg,max

. As a result, the ex ante probability of default, pt, at

a certain level of sovereign indebtedness, bgt , will be given by the cumulative distribution

function of the (generalized) beta distribution:

pt = Fbeta

(bgt4y

1

bg,max ;αbg , βbg

). (29)

5We will also, for the most part, assume that the labor tax rate remains constant, τwt = τw, and will stateexplicitly when we consider simulations in which this assumption is dropped.

6This implication of our setup is in line with evidence reported by Yeyati and Panizza (2011). Investigatingoutput growth across a large number of episodes of sovereign default, they find that the output costs of defaultmaterialize in the run-up to defaults rather than at the time when the default actually takes place.

12

Note that bg,max

denotes the upper end of the support for the debt-to-GDP ratio. Since we

keep the size of the haircut in case of default constant, we have

ϑt =

ϑdef with probability pt,

0 with probability 1− pt.(30)

Turning to monetary policy, we assume throughout that the central bank follows a Taylor-type

interest rate rule that also seeks to insulate aggregate economic activity from fluctuations in

risk spreads, at least to some degree. In particular, we assume:

log(1 + id,∗t ) = log(1 + id) + φΠ log(Πt/Π)− φω log((1 + ωt)/(1 + ω)). (31)

Here, id,∗t marks the target level for the deposit rate idt , and φΠ > 1, φω > 0. In deep

recessions, however, the target level and the actual deposit rate can diverge. The reason is

that in implementing rule (31), the central bank relies on steering the riskless nominal interest

rate idt , which cannot fall below zero. Therefore, idt = id∗t can only be implemented provided

that idt ≥ 0. Otherwise, idt = 0. As a result, an increase in the spread ωt cannot be offset if

monetary policy is constrained in lowering the policy rate.7

2.5 Market clearing and equilibrium

Good market clearing requires

yt =

∫ 1

0ct(i)di + gt + Ξtbt = πbc

bt + πsc

st + gt + Ξtbt. (32)

The total supply of output is given by

yt∆1/φt = zth

1/φt . (33)

7Although we focus here on a simple representation of monetary policy, the model would, in principle,allow for more complicated types of monetary policy. For example, a central bank faced with the ZLB couldpromise low future real rates to help the economy ease out of the lower-bound situation; see Eggertsson andWoodford (2003). This would not only increase output relative to the current interest rate rule (31), but itwould also raise tax revenues and therefore alleviate some of the fiscal strain. The question to what extentcentral banks can credibly engage in such forward guidance is not settled, however. Similarly, the effects ofother unconventional monetary policy operations, such as quantitative easing, are uncertain and likely to bebounded in practice.

13

In order to describe the equilibrium, we use equations (5)-(15), which characterize the solution

to the household problem; equations (16)-(19), which characterize financial intermediation;

equations (21)-(25), which characterize optimal price setting behavior; equations (26)-(30),

which characterize the behavior of fiscal policy; the assumption about the evolution of labor

taxes; the interest rate target rule (31) and the lower-bound constraint; and finally the good

market clearing conditions (32) and (33). For given exogenous realizations of et, gt, zt, these

equations pin down a sequence for the endogenous variables

bt, b

gt , c

bt , c

st , χt,∆t, Ft, ht, h

bt , h

st , i

bt , i

dt , i

d,∗t , igt ,Kt, λt, λ

bt , λ

st ,Λt,

ωt, pt, P∗

t /Pt,Πt, τwt , T

gt /Pt, trt, ϑt, wt,Ξt, yt .

2.6 Calibration

In order to solve the model numerically, we assign parameter values on the basis of observa-

tions for U.S. data. The relationship between sovereign risk, private-sector spreads, and the

debt level is calibrated based on cross-country evidence. A time period in the model is one

quarter.

With respect to monetary policy, we assume an average inflation rate of 2 percent per year.

The coefficient on inflation in the Taylor rule is set to a customary value of φΠ = 1.5. We

consider different values for parameter φω, the response of monetary policy to the interest

rate spread. The specific parameterization will be discussed in the respective sections below.

The steady-state level of government spending (consumption and investment) relative to GDP

is g/y = 0.2. The level of gross public debt in the steady state is set to 60 percent of annual

GDP. These values are broadly in line with U.S. averages over the last 20 years. In the baseline

scenario, we set distortionary tax rates to zero and assume that the adjustment of taxes over

the business cycle and in response to the debt level is achieved through lump-sum taxes. This

assumption allows us to focus on the main channels of transmission in a transparent way

while accounting for a feedback from economic activity to the fiscal outlook.8 We assume

that taxes react to debt sufficiently strongly (φT,bg large enough) so as to ensure that the

debt level remains bounded throughout and that φT,y = 0.34. This value is reasonable for

the U.S., but at the lower end of estimates for other OECD countries; compare Girouard and

Andre (2005).

8Below we explore the sensitivity of our results by also considering a distortionary tax rate on labor.

14

With regard to the preference parameters, we set the curvature of the disutility of work to

ν = 1/1.9, in line with the arguments provided by Hall (2009) regarding plausible values

for the Frisch elasticity of labor supply. We set an elasticity of demand of θ = 7.6 so as to

generate a gross price markup of µp = 1.15, which is in the range of customary values used

in the literature. Finally, we assume that the average intertemporal elasticity of substitution

σ = c/y, where σ := πb · (cb/y) · σb + πs · (c

s/y) · σs. If the model had a representative

household, this would correspond to the case of log-utility. Further, we assume that aggregate

hours worked in the steady state are given by h = 1/3. We choose the relative values of the

intertemporal elasticity of substitution for the two types of households (σb and σs) and of the

scaling parameters for the disutility of work (ψb and ψs) such that the linearized model can

be represented in the canonical three-equation New Keynesian format. This representation

allows us to derive a number of analytical results in the next section. Importantly, under

this calibration only the current value of the interest rate spread enters the dynamic IS-

relationship and the New Keynesian Phillips curve. In addition, the evolution of output and

inflation is independent of the level of private debt. Appendix A spells out in detail the

conditions under which this representation is valid. Specifically, given the other parameter

values, we set σb/σs = 0.53 and ψb/ψs = 0.82. We explore to sensitivity of our results with

respect to these assumptions through numerical simulations in Section 4.

We target a ratio of private debt to annual GDP, b/4y, of 80 percent, in line with Great Mod-

eration averages for the U.S. More precisely, the figure refers to nonfinancial, nonmortgage,

nongovernment credit market debt outstanding recorded in the U.S. flow of funds accounts.

The same target is used by Curdia and Woodford (2009). Along with the market clearing

condition, this determines scaling parameters ξb and ξs. Next, as in Curdia and Woodford

(2009), we assume that households redraw their type on average every 40 quarters, giving

δ = 0.975. This implies that the average time during which a specific type is without access

to payoff streams from asymptotic risk sharing is 10 years.

A central element in our calibration is the share of borrowers in the economy, πb. This

determines the share of economic activity that is affected by an increase in the spread and

therefore deserves some discussion. One possible calibration would refer to the (U.S.) Survey

of Consumer Finances. Averaging over the latest surveys (1998, 2001, 2004, and 2007), the

share of U.S. families that hold some kind of debt is 76 percent; compare Aizcorbe et al. (2003)

15

and Bucks et al. (2009). This suggests a value of πb = 0.76, and of πs = 0.24. However, loans

secured by the primary residence make up a large share of that debt. This suggests that such

a calibration for πb might overstate the importance of borrowing and the related effect that

an increase in borrowing spreads could have on economic activity. Another metric, also from

the Survey of Consumer Finances, that is more directly related to the notion of “borrowers”

and “savers” in our model is that on average 57 percent of families in the survey report

that – over the year preceding each survey date – they have been spending less than their

income, that is, they have saved. This suggests a value for πb of 1− 0.57, or πb = 0.43. That

said, both of the aforementioned figures do not explicitly take into account the borrowing by

firms in the economy (other than by single-owner firms). To the extent that households in

our model own firms and also make the intertemporal decisions for these firms, any purely

household-based measure of indebtedness is likely to underestimate the degree of indebtedness

and thereby the importance of the borrowing spread. In particular, using the same measure of

private borrowing as above (nonfinancial, nonmortgage, nongovernment credit market debt),

50 percent of private borrowing is accounted for by corporations rather than by households.

To capture this, we set πb = (1 − 0.17) · 0.43 + 0.17 · 1 = 0.53 in our baseline calibration.

This formula hypothetically divides households into consumption entities, some of which are

indebted, and investment entities, all of which have debt. In the calculations, 0.17 is the

share of nonresidential private domestic fixed and inventory investment in private domestic

economic activity.

In regard to the normal spread between deposit and lending rates, we target a steady-state

value of 2.1 percent (annualized), in line with commercial and industrial loan rate spreads

in the Federal Reserve’s Survey of Terms of Business Lending. This pins down parameter

χψ. The steady-state level for the central bank’s target interest rate, id, is set to 4.5 percent

annualized, from which the time discount factor, β, follows.

Turning to the production parameters, we set φ = 1, implying a linear production function.

We furthermore target a unit value for steady-state output; this pins down productivity, z.

We set parameter α = 0.9 in order to generate a slope of the Phillips curve in line with the

empirical evidence.9

9Specifically, our parameterization implies a slope coefficient of κ = 0.012. Galı and Gertler (1999) reportestimates for the slope of the Phillips curve, given by (1− βθ)(1− θ)/θ, in the range between 0.007 and 0.047.More recently, Altig et al. (2010) report an estimate of 0.014.

16

Figure 2: Sovereign risk premia vs. debt

GRE

IRL

POR

600

800

1000

1200

1400

1600

1800

r S

overe

ign C

DS

Spre

ad

poin

ts, as o

f M

ay 6

, 2011)

Fitted risk premium

AUS AUT BELCZE

DNKFIN

FRA

DEU

GRE

IRL

ITA

NLDNOR

POR

SLVSLO

ESP

SWE

GBR

USA0

200

400

600

800

1000

1200

1400

1600

1800

0 20 40 60 80 100 120 140 160

5-Y

ear

Sovere

ign C

DS

Spre

ad

(basis

poin

ts, as o

f M

ay 6

, 2011)

General Government Gross Debt(percent of GDP, forecast for 2011 and 2015)

Fitted risk premium

Notes: The figure shows 5-year sovereign CDS spreads against forecasts for end-2011 grossgeneral government debt/GDP (blue circles) and end-2015 debt/GDP (green triangles).The countries shown are Australia, Austria, Belgium, Czech Republic, Denmark, Finland,France, Germany, Greece, Ireland, Italy, Netherlands, Norway, Portugal, Slovak Republic,Slovenia, Spain, Sweden, United Kingdom, and United States. Excludes Japan. Forecastsare taken from the IMF World Economic Outlook April 2011.

Finally, it remains to determine the parameters that govern the spillover from sovereign risk

premia to private-sector spreads. Actual haircuts in case of a sovereign default show large

variation; see Panizza et al. (2009) and Moody’s Investors Service (2011). ϑdef = 0.5 appears

to be a reasonable average value. With respect to the specification of the fiscal limit, we

seek to replicate the relationship between the sovereign risk premium and public debt shown

in Figure 2. The figure plots CDS spreads of industrialized economies against the level of

projected gross debt of the general government (relative to GDP). The projections are taken

from the IMF’s World Economic Outlook in April 2011. The blue dots show projections for the

end of 2011. For comparison, the figure also plots IMF forecasts for the debt-to-GDP ratio by

the end of 2015. For the countries shown in the figure, CDS spreads are systematically higher

the higher the level of projected gross public debt.10 In fact, the risk premium appears to rise

10For a systematic empirical analysis of the relationship between fiscal variables and yields on governmentbonds, see, among others, Reinhart and Sack (2000), Ardagna et al. (2007), Baldacci et al. (2008), Haugh et al.(2009), Laubach (2009), Baldacci and Kumar (2010), or Borgy et al. (2011). Ardagna et al. (2007) explicitlyfocus on possible nonlinearities in the relationship and find that bond rates rise disproportionately for veryhigh levels of debt. Note, however, that sovereign risk premia are bound to be affected by more than justone fiscal variable, including such factors as the quality of fiscal institutions or the composition of the investorbase. We abstract from these complications to keep our exercise tractable and focus on the fact that highcurrent and/or projected debt is consistently found to be a key determinant of government financing costs.

17

disproportionately as the debt level rises. We choose parameters αbg = 3.70, βbg = 0.54, and

bg,max

= 2.56 to match this empirical relationship. The black solid line displays the implied

steady-state relationship between debt levels and the sovereign risk premium.

Regarding the spillovers from sovereign to private-sector risk, Figure 1 is suggestive of a

sovereign risk channel that runs from sovereign spreads to spreads in the household and cor-

porate sector. Of course, there might be other reasons for the observed comovement, too.

In the present paper, we abstract from these and interpret the comovement as caused by

sovereign risk, consistent with standard accounts of the sovereign debt crisis in parts of the

euro area. In regard to αψ, Harjes (2011) finds for a sample of large, publicly traded euro

area companies that a 100-basis-point increase in sovereign spreads raises private firms’ credit

spreads by about 50 to 60 basis points. As our baseline, we therefore set αψ = 0.55. Although

this value implies significant spillovers, it may still represent something closer to a lower bound

for two reasons. First, it is based on credit spreads of companies that are large, with often

sizeable export activities and access to international credit markets. Spillover effects from

sovereign risk are likely to be more pronounced for smaller and less international companies

that rely on local bank-based financing. Second, Figure 1 suggests that the comovement be-

tween spreads is considerably stronger in countries that face intense fiscal strain. Accordingly,

the value of αψ = 0.55 may understate the strength of the sovereign risk channel for highly

indebted countries. For these reasons, we also consider higher values as we move through the

simulations in the paper.

3 Sovereign risk, fiscal policy, and macroeconomic stability

In this section, we begin to analyze how sovereign risk affects macroeconomic dynamics and

stabilization policy in the model outlined above. Our focus is on the stability properties of the

economy, notably its vulnerability to self-fulfilling equilibria. In this context, we investigate

in detail how the sovereign risk channel alters the transmission of fiscal policy. We show

that monetary policy plays a key conditioning role, notably through its capacity to insulate

private borrowing costs from fluctuations in sovereign risk premia. To capture this aspect

we consider a scenario where monetary policy may be constrained by the ZLB. Our analysis

proceeds in two steps. First, in this section, we consider a special case of our model for which

we are able to obtain analytical solutions. For this case, we assume that the probability of

18

sovereign default depends on the expected primary deficit, rather than on the level of debt.

In the next section, we will turn to simulation-based results for the full model.

3.1 A tractable special case of the model

In this section, we focus on a first-order approximation of the equilibrium conditions around

the deterministic steady state. The aggregate equilibrium dynamics of the model can be

represented by a variant of the New Keynesian Phillips curve and a dynamic IS relationship.

The former relates inflation to expected inflation, output, and government purchases:

Πt = βEtΠt+1 + κy yt − κggt, (34)

where κy = κ(ν + σ−1) and κg = κσ−1, with κ = (1−α)(1−αβ)α .11 In terms of notation,

yt = yt − y, gt = gt − g, and Πt = log(Πt/Π), where variables without a time subscript refer

to steady-state values.

The dynamic IS-relationship links output to real government spending and the effective real

interest rate through

yt − gt = Etyt+1 − Etgt+1 − σ[idt + (πb + sΩ) ωt − EtΠt+1 + Γt

], (35)

where ωt := log((1+ωt)/(1+ω)), idt := log((1+ idt )/(1+ i

d)), and Γt := Et log(et+1)− log(et).

From the IS relationship, it is clear that fluctuations in the private-sector spread can in-

fluence economic activity unless they are neutralized by monetary policy. The degree to

which the private-sector spread affects economic activity, for a given policy rate, is deter-

mined by parameters πb + sΩ. As discussed in Curdia and Woodford (2009), parameter

sΩ := πbπs(σb cb/y − σs cs/y)/σ indicates the extent to which interest rate increases affect

the aggregate demand by borrowers more adversely than that of savers. In our calibration,

cb > cs and sΩ > 0.

As regards monetary policy, equation (31) implies that during normal times (in deviations

from steady state):

idt = φπΠt − φωωt. (36)

11Here, as in the following linearizations, we abstract from fluctuations in productivity, zt.

19

For the analytical results, we initially consider the case φω = (πb + sΩ), in which the central

bank fully neutralizes the effect of the sovereign risk premium on aggregate economic out-

comes, as apparent from the IS equation (35). However, monetary policy may not always be

able to do so. In particular, we assume below that monetary policy becomes constrained such

that the nominal interest rate is stuck at the lower bound of zero in the initial period of our

simulations. This means that the central bank can no longer offset a rise in the interest rate

spread. We follow Christiano et al. (2011) and Woodford (2011) in assuming that monetary

policy will return to Taylor rule (36) in the next period and be unconstrained thereafter with

probability 1 − µ, where µ ∈ (0, 1). Otherwise, the zero interest rate persists into the next

period. The same Markov structure applies for the remaining periods. As a result, the ex-

pected length of the ZLB episode is given by 1/(1 − µ). Shocks to the time discount factor,

Γt, follow the same Markov structure.12 Given that there are no endogenous state variables

in the special case of our model considered here, once the ZLB situation ceases to persist, the

economy immediately reverts to the steady state.

As indicated above, we make one further simplifying assumption in this section that allows us

to derive analytical results. Specifically, we assume that the probability of sovereign default—

and thus the sovereign risk premium—depends on the expected primary deficit rather than

the level of public debt as in the full model. Consequently, the interest rate spread also

depends on the expected deficit. We postulate a linear relationship of the form

$t = ξEt(gt+1 − φT,yyt+1), (37)

where, in order to ease the burden on notation, we have defined the spread that enters the IS

relationship over and above the risk-free deposit rate as $t := (πb + sΩ)ωt. Parameter ξ ≥ 0

indicates the extent to which fiscal strain—as measured by primary deficits—spills over to

private-sector spreads. Parameter φT,y ∈ [0, 1) measures the sensitivity of tax revenue with

respect to economic activity.

12Specifically, we assume a temporary increase in the effective discount factor, triggered by 0 < et = eL < 1while at the ZLB, so Γt = µ log(eL)− log(eL) = −(1− µ) log(eL) ≥ 0.

20

Table 1: Quantifying parameter ξ

ξ by length of ZLB episode (qtrs)

Debt/GDP ξ′ 6 7 8

60 percent 0.0005 0.004 0.005 0.005

90 percent 0.0016 0.014 0.015 0.017

110 percent 0.0030 0.025 0.028 0.031

130 percent 0.0051 0.042 0.047 0.052

140 percent 0.0065 0.054 0.060 0.066

150 percent 0.0083 0.068 0.076 0.084

Notes: The table presents estimates for the slope of the average private interest ratewith respect to the fiscal deficit, ξ, for different average lengths (in quarters) of the ZLBepisode and for different debt/GDP ratios. The entries in the columns ”ξ by length of

ZLB episode (qtrs)” are based on the formula ξ = 1+µ(1−µ)µ(1−µ)

ξ′ that is explained in detailin the main text and in Appendix B.

3.2 The size of the spillover from public to private risk premia

To appreciate our results below, it is useful to discuss the range of plausible values for ξ in

equation (37), which—through a sequence of back-of-the-envelope calculations—links to the

fundamental parameters of the model. Let ξ′ be the slope of the risk premium with respect

to debt at a specific debt level, evaluated in the steady state. Our assumptions regarding the

sovereign spread in Section 2, in particular equation (29), imply that

ξ′ = αψ(πb + sΩ)ϑdef

1− ϑdef Fbeta

(bg

4y1

bg,max ; αbg , βbg

) 1

4y

1

b g,maxfbeta

(b

4y

1

bg,max ; αb, βb

). (38)

The first column of Table 1 reports the resulting values for ξ′ at different debt levels using

the calibration of the fiscal limit distribution discussed in Subsection 2.6.

These values appear to be fairly small. It needs to be borne in mind, however, that the

relationship in equation (37) links the interest rate spread to the expected deficit, whereas

the full model implies a link between the interest rate spread and the expected level of

debt, i.e., the result of a series of accumulated deficits. The values for ξ′ are thus bound

to understate the sensitivity of the interest rate spread to a persistent fiscal deficit. More

precisely, an appropriate mapping from the slope of the risk premium into the simplified

model environment needs to take into account the horizon over which deficits accumulate.

The following expression is meant to capture this fact for empirically reasonable values of

21

µ > 0.5 (so the ZLB is expected to be binding for at least two periods):13

ξ =1 + µ(1− µ)

µ(1− µ)ξ′. (39)

The columns under “ξ by length of ZLB period” in Table 1 report the corresponding values

of ξ for different initial debt levels if the ZLB has an expected duration of six, seven, or eight

quarters. These calculations suggest that a value of ξ as high as 0.1 cannot be ruled out

if the initial debt stock is large and the recessionary shock persists for an extended period.

In particular, recall from Figure 1 that the spillovers may be noticeably stronger than usual

for countries that face intense fiscal strain. A bigger spillover parameter, αψ, would scale up

linearly the entries in Table 1.

3.3 Sovereign risk channel and equilibrium determinacy

Assume, as a baseline scenario, that the level of government spending is exogenously given.

For this case, we find that the sovereign risk channel significantly alters the determinacy

properties of the model while the ZLB is binding. Specifically, the range of parameters that

ensure determinacy shrinks in the presence of sovereign risk. In the following, we establish

distinct restrictions on parameters that yield a (locally) determinate equilibrium.14

Proposition 1 In the economy summarized by equations (34) – (37), let the interest rate be

equal to zero in the initial period. In each subsequent period, let the interest rate remain at

zero with probability µ ∈ (0, 1). Otherwise, let monetary policy be able to permanently return

to Taylor rule (36). There is a locally unique bounded equilibrium if and only if

a) a < 1/(βµ), and b) (1− βµ)(1− a) > µσκy,

where a := µ+ µξφT,yσ and κy := κ[ν + 1/σ].

Proof. See Appendix C.

In the absence of an endogenous risk premium (i.e., for ξ = 0) as in Christiano et al. (2011)

and Woodford (2011), condition a) is always satisfied. Hence there will be a unique bounded

13Appendix B presents a more detailed motivation of the following formula.14We focus on local determinacy once the economy has reached the ZLB. A separate strand of the literature

examines global determinacy in the New Keynesian model. Benhabib et al. (2002), for example, propose afiscal policy setup that rules out liquidity traps by making the low-inflation steady state fiscally unsustainable.Mertens and Ravn (2011) study the efficacy of fiscal policy in belief-driven equilibria.

22

equilibrium if and only if condition b) holds. If ξ = 0, condition b) is given by (1−βµ)(1−µ) >

µσκy. The previous literature has shown that the set of “fundamental” parameters for which

this condition holds is larger (i) the less persistent the ZLB situation (in our parameterization,

the smaller µ); (ii) the lower the interest sensitivity of demand (the smaller σ); and (iii) the

flatter the Phillips curve (the smaller κy). In addition to these findings, our analysis shows

that the range of parameters for which the equilibrium is determinate shrinks in the presence

of a sovereign risk channel. Specifically, with ξ > 0, condition a) is violated if either the

interest rate spread is sufficiently responsive to the deficit or if tax revenue is sufficiently

responsive to output (φT,y is large enough). Note that the same parameters are also key

determinants for whether condition b) is satisfied.15

It is instructive to contrast this baseline result with a situation where government spending

adjusts endogenously to output while the economy is at the ZLB. The following proposition

summarizes the pertinent conditions for the existence of a unique bounded equilibrium.

Proposition 2 In the economy specified in Proposition 1, let government spending gt take on

a value of gt = ϕyt when the economy is at the ZLB, and gt = 0 otherwise. Suppose further

that ϕ < 1. Define a∗ := µ+µξφ∗T,yσ∗; κ∗y = κy −ϕκg; φ

∗

T,y := φT,y −ϕ; and σ∗ = σ/(1−ϕ).

There exists a locally unique bounded equilibrium if and only if:

1. with a∗ > 0

a) a∗ < 1/(βµ), and b) (1− βµ)(1− a∗) > µσ∗κ∗y,

2. with a∗ < 0:

a) (1 + βµ)(1 + a∗) > −µσ∗κ∗y and b) (1− βµ)(1− a∗) > µσ∗κ∗y.


15The analytical results in Proposition 1 do not depend on the strength of the response to inflation, φπ,once the economy has left the ZLB (apart from whether the parameter satisfies the Taylor principle). Atfirst glance this seems to contradict the results in Davig and Leeper (2007). Yet, these authors study aneconomy with monetary regime changes in which the Taylor principle is satisfied in one regime but not theother. They show that the equilibrium may remain locally determinate in both regimes if the “passive regime”is not too persistent and if—in addition—monetary policy is sufficiently responsive to inflation in the “active”regime. This suggests that the monetary response to inflation should enter the determinacy conditions. Theircalculations, however, explicitly exclude the possibility that the passive regime entails a ZLB scenario in whichmonetary policy does not react at all to inflation. Instead, they assume some reaction of monetary policy toinflation in both regimes. If one of the regimes entails a ZLB situation, the precise strength of the response toinflation in the active regime does not feature in the determinacy conditions.

23

To appreciate the implications of this proposition, consider first the possibility that there is no

sovereign risk channel (ξ = 0). In this case the range of parameters for which the equilibrium

is determinate is larger if spending is countercyclical (ϕ < 0). With an endogenous risk

premium, however, the opposite may hold. More precisely, if ξ > 0 and if, in addition, the

conditions of Item 1 of Proposition 2 hold, then subject to some limits on the elasticity of taxes

with respect to output, namely, φT,y < 1− κν(1−βµ)ξ , the range of fundamental parameters for

which the equilibrium is determinate is at least as large with a procyclical spending response,

ϕ ∈ (0, 1), as without any response; indeed the range can even be larger. Note that this case

is more likely the lower the elasticity of tax revenue to economic activity (the smaller φT,y),

and the more strongly the interest rate spread responds to the deficit (the larger ξ). The

main conclusion is straightforward, if unconventional: a procyclical fiscal stance may reduce

the risk of equilibrium indeterminacy in the presence of sovereign risk.16

The two propositions above deserve some further discussion. While previous work has focused

on the case in which government debt and a rising risk premium imply explosive debt, we

consider a situation in which debt ultimately will always be stabilized through one-off tax

measures (although sovereign default can still occur). In such an environment, we find that

an economy with an endogenous risk premium and a constrained central bank can be prone

to belief-driven equilibria. Moreover, we find that systematic spending cuts during recessions

(when the ZLB is binding) may actually help to anchor expectations to a unique equilibrium.

To see why, assume that during the ZLB period agents expect some drop in output. Lower

output means less tax revenue and, in the absence of a fiscal response, higher deficits, which

in turn imply a higher interest rate spread. As the widening of the interest rate spread

cannot be offset by monetary policy at the ZLB, the real interest rate rises. Consequently,

expectations of adverse output developments can become self-fulfilling in high-debt economies

where a high and rising interest rate spread weighs heavily on output, thus confirming agents’

beliefs in equilibrium. By contrast, a procyclical fiscal stance may be sufficient to prevent an

adverse expectational shock from confirming itself, because public spending cuts would offset

the expected decline in tax revenue triggered by a fall in output.

16(See Appendix D, Corollary 4 for details). It bears stressing that we focus here on very simple fiscaland monetary rules in order to maintain analytical tractability. More complicated rules that would makefuture monetary or fiscal behavior depend on past developments might, in principle, help overcome problemsof indeterminacy.

24

Figure 3: Determinacy regions with endogenous response of government spending

Different expected durations of the ZLB episodeϕ(gt=ϕy t)

6 quarters 7 quarters 8 quarters

0 0.1 0.2 0.3 −1

−0.8

−0.6

−0.4

−0.2

0

0.2

0.4

0.6

0.8

Procyclicalresponse

Countercyclicalresponse

0 0.1 0.2 0.3 −1

−0.8

−0.6

−0.4

−0.2

0

0.2

0.4

0.6

0.8

Procyclicalresponse


0 0.1 0.2 0.3 −1

−0.8

−0.6

−0.4

−0.2

0

0.2

0.4

0.6

0.8

Procyclicalresponse


Notes: Determinacy regions with endogenous response of government spending to economic activity during a deeprecession. Grey areas mark parameterizations that imply determinacy. y-axis: response of government spendingto output, ϕ (gt = ϕyt). x-axis: response of the interest rate spread to the deficit, ξ. From left to right: ZLB isexpected to bind for 6, 7, or 8 quarters (µ = 5/6, 6/7, 7/8).

Figure 3 illustrates the results of Propositions 1 and 2 for the baseline parameterization.

Each panel of the figure displays results for a different value of µ implying, from left to

right, an expected duration of the ZLB episode of 6, 7, and 8 quarters, respectively. We

evaluate whether a unique equilibrium exists for different values of the slope of the risk

premium, ξ, measured on the horizontal axis, and the response of government spending to

output, ϕ, measured on the vertical axis. Grey areas indicate determinacy regions, while

white areas indicate equilibrium indeterminacy. In the case of protracted ZLB episodes (right

panel) with a steep slope of the risk premium, we find that there may be no countercyclical

spending policy—of the simple form analyzed here—that ensures determinacy. However, a

policy of procyclical spending cuts is not a panacea either; although it is helpful under the

circumstances detailed above in reducing the risk of belief-driven equilibria, it does not ensure

determinacy for all values of ξ under consideration.

On a final note, we have made the risk premium depend on the expected next-period deficit in

this section, as apparent from (37). This conforms to the notion that sovereign spreads reflect

a forward-looking assessment of the fiscal position. Quantitatively, however, it turns out that

our results would be very similar if we had assumed that the sovereign spread depends on the

current period’s deficit.

25

3.4 Output effects of government spending cuts

In the following we shift our focus to the output effects of exogenous government spending

cuts. To that end, we limit our analysis to parameterizations for which a stable and unique

equilibrium exists. Our results suggest that sovereign risk is a key determinant for the size,

and even sign, of the fiscal multiplier. In the simplified model setup that we consider at

the moment, the sovereign risk channel is governed by parameter ξ. However, since mone-

tary policy may neutralize the effects of the sovereign risk channel outside the ZLB episode,

parameter µ plays a key role in our analysis as well.

Following Woodford (2011) and Christiano et al. (2011), we focus on an economy at the ZLB

and assume that government spending deviates from its steady-state level during the ZLB

episode only, i.e., by taking on a value of gt = gL. Otherwise government spending is set to

its steady-state level. Our key result is summarized by the following proposition.

Proposition 3 Under the conditions spelled out by Proposition 1 (which ensure that a locally

unique bounded equilibrium exists), let shock Γt take on a value of Γ for as long as monetary

policy is constrained to zero interest rates, and a value of 0 otherwise. Similarly, let govern-

ment spending take on a value of gL when the economy is at the ZLB, and 0 otherwise. As

before, define a = µ+µξφT,yσ, and b = µ+µσξ. Then, while monetary policy is constrained,

output is given by

yL = ϑr(log(1 + id)− Γ) + ϑg gL,

where

ϑr =σ(1− βµ)

(1− βµ)(1 − a)− µσκy> 0 (40)

and

ϑg =(1− βµ)(1 − b)− µσκg(1− βµ)(1− a)− µσκy

. (41)


Note that ϑg provides a measure for the government spending multiplier on output at the

ZLB. It is characterized in more detail by Corollary 5 in Appendix D.2. Specifically, under

the determinacy conditions established above, equation (41) implies that the multiplier is

positive if and only if

(1− µ)−µσκg1− βµ

> µξσ. (42)

If this condition is satisfied, a spending cut at the ZLB will reduce output, in line with

conventional wisdom. If ξ = 0, i.e., in the absence of a sovereign risk channel, this will always

26

Figure 4: Effects of early retrenchment

Output Deficit Interest rate spread

Notes: The figure shows the effects of a unit cut in government spending for the length of the ZLB episode. Effecton output (left panel), on the deficit (middle panel: negative means the deficit shrinks), and on the interest ratespread (right panel). On the axes: responsiveness of interest spread to expected deficit, ξ, and expected durationof ZLB episode: 1/(1 − µ). Only parameterizations that imply determinacy are shown. For better readability,multipliers and deficits are capped at the maximum level indicated in the charts.

be the case. Moreover, the government spending multiplier will be strictly greater than one,

consistent with the analysis of Christiano et al. (2011) and Woodford (2011). In contrast, if

ξ > 0, the government spending multiplier at the ZLB may actually become negative, such

that spending cuts raise output.

The left panel of Figure 4 illustrates this result. It displays the output effect of a government

spending cut during the ZLB episode for different levels of spillovers from sovereign risk, as

measured by alternative values for ξ, and for different assumptions regarding the expected

length of the recession, as measured by alternative values for 1/(1−µ). The other parameters

underlying these computations remain fixed as laid out earlier. In the same figure we also

show the response of the budget deficit (middle panel) and the interest rate spread (right

panel).

The figure shows that the fiscal multiplier depends crucially on both dimensions under con-

sideration. Consider first the case where ξ = 0, that is, a situation when there is no sovereign

risk channel. In this case, a spending cut invariably causes a sizeable decline in output. In

fact, for an expected duration of the ZLB episode of eight quarters, the government spending

multiplier on output reaches a value as high as 3, a result recently stressed in Christiano

27

et al. (2011). The underlying mechanism is well understood: the deflationary effect of spend-

ing cuts cannot be counteracted by a reduction in policy rates, thus causing an increase in

the real interest rate which crowds out private demand. The effect is stronger the longer the

expected duration of the ZLB episode, as private demand is determined by the expected path

of current and future short-term real interest rates.

Turning to the scenario of an active sovereign risk channel, we focus first on a case where the

ZLB period is expected to be short, namely four quarters only. In this case, as the interest

rate spread becomes more responsive to the fiscal deficit, i.e., as ξ takes on bigger values, the

fiscal multiplier tends to decline. In other words, output falls by less in response to a public

spending cut. Still, the role of the sovereign risk channel is limited, even for very high values

of ξ. This is due to the fact that monetary policy is expected to be able to offset the effect of

sovereign risk on private interest rates in the near future.

The picture changes significantly if monetary policy is expected to be constrained for an

extended period. Under those circumstances, the sovereign risk channel has a strong bearing

on the fiscal transmission mechanism. In fact, if ξ and µ both take on sufficiently high values,

the sign of the output multiplier turns negative, implying that a spending cut during the

ZLB episode becomes expansionary. To understand this finding, it is useful to consider the

responses of the deficit and the risk premium. Note that for almost all parameterizations, a

cut in government spending reduces the deficit (see also Erceg and Linde (2010b)). If fiscal

strain is severe at the outset, the lower deficit leads to a considerable decline in the risk

premium. This, in turn, reduces the interest rate spread, stimulates private demand, and

raises tax revenue. The result is a virtuous cycle of an additional decline in interest rate

spreads, increased economic activity, and a further improvement of the fiscal outlook.17

In sum, our simplified model setup reveals a potentially important role for the sovereign risk

channel. Although the model implies standard positive multipliers under normal conditions

(i.e., public spending cuts depress short-term output), fiscal retrenchment may become less

contractionary, and even turn expansionary, in the presence of severe fiscal strain if monetary

policy is unable to cushion the adverse effects of sovereign risk on private-sector borrowing

conditions.

As such, our results shed some fresh light on the theoretical possibility of ”expansionary fis-

17Contrary to the first impression given by Figure 4, conditional on the length of the ZLB episode the sizeof the multiplier is monotone in the responsiveness of the spread to the deficit, as measured by parameter ξ.

28

cal contractions,” which has attracted significant attention following the prominent study by

Giavazzi and Pagano (1990), who consider the experience of Denmark and Ireland during the

1980s.18 In order to rationalize expansionary consolidations, previous theoretical accounts

have often focused on the “expectations view,” whereby immediate fiscal retrenchment trig-

gers a shift in expectations regarding the long-run level of spending, and thus a downward

revision of the anticipated tax burden (Bertola and Drazen 1993, Sutherland 1997, and Per-

otti 1999). In a similar vein, Blanchard (1990) formalizes the idea that early consolidation

may reduce the likelihood of more disruptive future adjustment, thus boosting current pri-

vate spending. Giavazzi and Pagano themselves stress that monetary policy may also have

played an important role in the Danish and Irish episodes. Specifically, both episodes were

marked by credible exchange rate pegs, which arguably led to declining country risk premia

and lower real interest rates. More recently, Erceg and Linde (2010a) have analyzed govern-

ment spending cuts in a model of a currency union where country risk is a function of the

state of public finances.19 Our own analysis provides a novel contribution to this literature

by highlighting a distinct set of economic conditions—high sovereign risk and a constrained

central bank—under which spending cuts may have non-standard effects.20

4 Dynamic analysis

We now turn to a numerical analysis of the full model as outlined in Section 2 above. This

allows us to revisit our analytical results while accounting for the possibility that sovereign

risk depends on the expected debt level rather than the expected deficit. In order to highlight

the role of monetary policy, we focus again on a ZLB scenario. However, we depart from the

18The evidence on expansionary consolidations remains controversial. For a positive assessment, see, forexample, Alesina and Perotti (1995) or Alesina and Ardagna (2010). A skeptical view is presented by Inter-national Monetary Fund (2010b). Perotti (2011) provides a reassessment.

19In simulations, they find that output always falls in the initial periods of a persistent spending cut but thatthe effects may eventually turn positive during the dynamic adjustment process. For high levels of debt we ob-tain even stronger results—notably positive impact effects—as we consider a wider range of parameterizationsand allow for a nonlinear relationship between the risk premium and the level of public debt.

20Earlier papers have also shown that the expectation of persistent fiscal retrenchment after the ZLB episodecan stimulate economic activity while the economy is still at the ZLB; see, for example, Corsetti et al. (2010) andWoodford (2011). Appendix E discusses how the sovereign risk channel affects those results. For the scenariosunder consideration, we find that there are parameterizations for which expected future retrenchment increasesoutput at the ZLB in the presence of a sovereign risk channel, while it crowds out output in the absence ofsuch a channel. The reverse does not hold. In particular, whenever a future retrenchment package is found toboost output at the ZLB in the absence of sovereign risk, it also boosts output at the ZLB in the presence ofsovereign risk. Indeed, any positive output effect caused by expected future retrenchment is even stronger ifthe sovereign risk channel is active.

29

simplifying assumption that the expected duration of the ZLB episode is constant. Instead,

we envisage a scenario in which a) the initial debt level matters for the depth of the recession;

and b) fiscal retrenchment may alter the length of the ZLB episode.21

4.1 Deep recessions and sovereign risk

To set the stage for our analysis, we subject the model economy to a large shock that pushes

monetary policy to the ZLB. Specifically, we consider a first-order autoregressive process for

et to capture in a stylized manner the output loss in the U.S. during the 2007–2009 recession.

The Congressional Budget Office (2011) estimates that the output gap reached 6.7 percent in

2009 and that it will still be at a 1.7 percent level in 2014 and at 0.5 percent in 2015.22 For

the simulations, we also assume that taxes stabilize the debt level, if only very gradually.23

While the simulations for the baseline scenario assume that taxes are raised in a lump-sum

manner, Subsection 4.3 assesses the extent to which distortionary taxation would affect our

conclusions.

Figure 5 shows the evolution of output, the interest rate spread, and the policy rate in

response to the recessionary shock. It displays the behavior of the economy in the absence of

any discretionary fiscal policy measure for three different initial levels of government debt: 60

percent of GDP (black solid line), 90 percent (blue dashed line), and 115 percent (red dots).

The adjustment dynamics differ substantially in that the decline in output and the rise of the

interest rate spread are much stronger if initial debt is high. To understand this result, note

that the shock induces an increase in the budget deficit, which leads to a build-up of public

debt and thus an increase in the sovereign risk premium. Moreover, since the shock pushes the

economy to the ZLB, monetary policy is unable to offset the spillover from sovereign risk to

private interest rates. Private expenditure thus falls further, compounding the initial decline

in output. This effect is stronger the higher the initial debt level, because the relationship

21We solve the model economy under perfect foresight using standard techniques.22Given the process log(et) = ρe log(et−1) + ut, we set u0 = −0.1525 (with ut = 0 for all other periods)

and ρe = 0.93 to roughly replicate those values for our baseline economy with a debt-to-GDP ratio of 60percent. At the time of writing, the CBO had not yet published output gap estimates and forecasts based onthe revision to the national income and product accounts released by the BEA on July 29, 2011.

23In particular, unless noted otherwise, we set the response parameter φT,bg = 0.014 for the first 30 quarters.This response is twice as large as would be required to ensure stable debt dynamics in the absence of adversemovements in the risk premium. At the same time, the adjustment of taxes is slow enough that withoutgovernment spending cuts, the debt burden would stabilize in a very gradual manner only. Beyond quarter30, φT,bg rises to twice the previous value, ensuring that government debt will eventually be stabilized evenfor the higher level of indebtedness (and a correspondingly higher risk premium) prevailing at that point.

30

Figure 5: Deep recession with different initial levels of government debt

Output (% from ss) Interest rate spread (bps) Policy rate (%)

0 5 10 15 20 25−15

−10

−5

0

60% debt/GDP90% debt/GDP115% debt/GDP

0 5 10 15 20 250

200

400

600

0 5 10 15 20 25

1

2

3

Notes: The figure shows responses to the recessionary shock for different initial debt levels. Black solid line:60 percent debt-to-GDP, blue dashed: 90 percent, red dots: 115 percent. Output is expressed in terms ofpercent deviations from the steady state, the risk premium in annualized basis points, and the interest ratein annualized percentage rates.

between public debt and sovereign risk is fundamentally nonlinear.

In our simulations, a persistently high risk premium also lengthens the time span over which

the ZLB remains binding. This result is apparent from the dynamics of the policy rate shown

in the right panel of Figure 5: the ZLB episode is extended by as much as 11 quarters if

government debt is high. Hence, our dynamic analysis delivers a first additional insight:

not only does the importance of the sovereign risk channel depend on whether the central

bank is constrained in steering interest rates, but sovereign risk may itself be an important

determinant for how severely monetary policy is constrained in the face of certain shocks.

4.2 Fiscal retrenchment during deep recessions

What are the effects of government spending cuts in the recessionary environment just de-

scribed? In order to mimic the setup of Section 3, we consider an episode of fiscal restraint

that lasts for two years and starts at the onset of the recession, that is, we consider an “imme-

diate retrenchment” scenario. We discuss alternative timing assumptions in Subsection 4.3.

During the episode of fiscal restraint, government spending falls below its steady-state level

by 2 percent of (steady-state) GDP. Figure 6 depicts the resulting dynamics relative to the

baseline scenario. The panels on the left show the response of output (top) and the interest

rate spread (bottom). In order to isolate the effect of a binding ZLB, the panels in the middle

and on the right show the response of the same variables under the assumption that the exit

31

Figure 6: The impact—relative to the baseline—of immediate retrenchment

Timing of ZLB exit endogenous ZLB lasts for 7 quarters ZLB lasts for 18 quarters

a) Effect on output (% deviation from ss)

0 5 10 15 20 25

−2

−1

0

1

2


0 5 10 15 20 25

−2

−1

0

1

2

0 5 10 15 20 25

−2

−1

0

1

2

b) Effect on risk premium (bps, annualized)

0 5 10 15 20 25−200

−150

−100

−50

0

0 5 10 15 20 25−200

−150

−100

−50

0

0 5 10 15 20 25−200

−150

−100

−50

0

Notes: The panels show the effects of an immediate retrenchment in government spending by 2 percentof steady-state output for 8 quarters on output (top) and the risk premium (bottom). Solid black line:60% initial debt-to-GDP ratio, dashed blue line 90%, dotted red line: 115%. Left panel: the effect of theretrenchment when the timing of the exit from the ZLB is endogenously determined according to equation(36). Other panels: for each initial debt level, the depth of the recession without retrenchment is calibratedsuch that it implies a binding ZLB for 7 quarters (middle) and 18 quarters (right). For the middle andrightmost panels, regardless of the austerity package being implemented, monetary policy is assumed to keepthe nominal rate at zero for that time period (7 and 18 quarters, respectively).

32

from the ZLB is not endogenous, but fixed exogenously at 7 and 18 quarters. These lengths

correspond, respectively, to the duration of the ZLB episode for debt-to-GDP ratios of 60

percent and 115 percent in Figure 5.24

We find, first, that for all initial debt levels, the retrenchment package is effective in reducing

the deficit (not shown). Thus, the level of government debt and the risk premium (consistent

with Figure 4) decline. In addition, monetary policy escapes from the ZLB constraint some-

what earlier for all debt levels (not shown). However, the spending cuts have quite different

effects on output across our different scenarios. If initial debt is low, the spending cuts prompt

an initial output decline of more than 2 percent, as private expenditure also falls. In contrast,

if initial debt is high, the initial output response is actually positive, reflecting a strong in-

crease in private expenditure. To understand this finding, recall that spending cuts affect real

interest rates through two channels. On the one hand, the deflationary effect of lower public

spending raises, all else equal, real interest rates as it cannot be offset by a reduction in pol-

icy rates at the ZLB. On the other hand, the reduction of public debt reduces sovereign risk,

thereby lowering private interest rate spreads. The strength of the effect operating through

the second channel increases in the initial level of debt, as the postulated relationship between

public debt and sovereign risk is nonlinear. In our simulations, this sovereign risk channel

turns out to be dominant if we assume an initial debt level of 115 percent of GDP.

As stressed above, the impact of the recessionary shock and the period of time for which

monetary policy is constrained depend on the initial level of debt. In addition, the initial

level of debt also determines the quantitative importance of the sovereign risk channel. To

isolate the latter dimension, the panels in the middle and right columns of Figure 6 show the

effect of the austerity packages on output for different debt levels, but fixing the length of

the ZLB episode exogenously. If the lower bound is expected to be binding only for a short

period of time (middle panels), the effect of the spending cuts hardly varies with the debt

level. In other words, the importance of sovereign risk appears limited. However, in line with

our earlier results in Section 3, the picture changes quite dramatically if the lower bound is

expected to be binding for an extended period of time (right panels). In this case, we find that

spending cuts have a positive and lasting effect on economic activity at high initial levels of

debt, which under our specification imply elevated sovereign risk premia (dotted red line, right

24In the underlying computations, for each debt level, we rescale the initial recessionary shock such that theZLB binds for the desired length of time.

33

panel). Moreover, the ”output costs” of public spending cuts are noticeably lower than usual

even for the intermediate, 90 percent, level of debt to GDP (dashed blue line in the rightmost

panel). Overall, we thus find our earlier analytical results confirmed by the simulations of the

full-fledged model: fiscal strain alters the fiscal transmission mechanism through the sovereign

risk channel, provided that monetary policy is constrained for an extended period.

4.3 Further considerations

This section assesses the sensitivity of the previous results with respect to some modifica-

tions that may have a bearing on the sovereign risk channel. We start by assessing how an

alternative timing of spending cuts affects the impact of fiscal retrenchment. We then explore

alternative assumptions on the tax system and on the conduct of monetary policy.

4.3.1 The timing of spending cuts

So far, we have focused on spending cuts that take place immediately, i.e., at the time the

recessionary shock hits the economy. This scenario reflects an important premise guiding the

analysis in this paper: namely that policymakers facing nonnegligible sovereign risk premia

will generally find it difficult to improve investor confidence solely by announcing future aus-

terity. More likely, investors concerned about default risk will expect to see some immediate

proof of policymakers’ readiness to cut deficits, thus prompting upfront tightening measures.

Nevertheless, it is worth contrasting the effect of such immediate tightening programs with

examples of more backloaded deficit reduction. We now assess the role of such timing deci-

sions on the basis of model simulations. The left panels of Figure 7 reproduce the results for

an immediate retrenchment that were reported in the left column of Figure 6. The remaining

columns report the impact of two alternatively timed (and sized) consolidation packages. The

middle panels display the response of the economy to a package of spending cuts of 2 percent

of steady-state GDP that starts two years after the initial recessionary impact and that lasts

for 10 years (a “medium-term retrenchment”). The right panels, in turn, show results for a

combination of the previous two packages (a “persistent retrenchment,” that sees spending

cuts start immediately and last for 12 years in total). As before, the figures report the effect

of these different packages depending on the initial level of debt (the range of the axes has

been rescaled to accommodate the range implied by these simulations).

34

Figure 7: The timing of retrenchment

Immediate retrenchment Medium-term retrenchment Persistent retrenchment

a) Effect on output (% deviation from ss)

0 5 10 15 20 25−2

0

2

4


0 5 10 15 20 25−2

0

2

4

0 5 10 15 20 25−2

0

2

4

b) Effect on interest rate spread (bps, annualized)

0 5 10 15 20 25−400

−300

−200

−100

0

0 5 10 15 20 25−400

−300

−200

−100

0

0 5 10 15 20 25−400

−300

−200

−100

0

Notes: The panels show the effect of a retrenchment in government spending by 2 percent of steady-stateoutput on output (top) and the risk premium (bottom) for different assumptions on the timing of the austerityepisode. Left panels: immediate retrenchment for first 2 years; middle: medium-term retrenchment (duringyears 3 through 12), right: persistent retrenchment for 12 years. Solid black line: 60% initial debt-to-GDPratio, dashed blue line 90%, dotted red line: 115%. For all the panels the timing of the exit from the ZLB isendogenously determined according to equation (36).

Under medium-term retrenchment (middle panels), there are immediate output gains from

fiscal forward guidance, in line with the results in Corsetti et al. (2010). Specifically, most

or all of the spending cuts are implemented when monetary policy has escaped from the

ZLB constraint and regained its ability to contribute to economic stabilization. When the

spending cuts occur, they reduce contemporaneous demand and inflation, causing the central

bank to lower the real interest rate. The prospect of a lower future real rate already crowds

in consumption, and thus output, during the early periods of the recession, i.e., before the

government spending cuts occur. This leads to higher tax revenue and implies an immediate

reduction in the sovereign risk premium, which further stimulates demand through reduced

35

interest rate spreads facing the private sector. Note that such anticipated medium-term

retrenchment unfolds a stronger expansionary effect upfront, the weaker the initial fiscal

situation (dotted red line vs dashed blue line in the central panels).

The persistent retrenchment scenario, in turn, is a combination of the two previous scenarios.

In the simulations shown in the right column of Figure 7, persistent retrenchment has the

strongest effect on the risk premium (red dotted line), reflecting the larger overall cut to

spending. However, its output effects are generally somewhat smaller than in the medium-

term retrenchment scenario. For the highest level of debt under consideration (i.e., 115

percent of GDP), the persistent retrenchment still crowds in economic activity for most of

the time that the economy remains constrained by the ZLB. However, the initial boost to

output is more subdued than under medium-term retrenchment, because the impact from

the additional reduction in debt—and hence the risk premium—is more than offset by the

immediate contractionary effect of upfront spending cuts.

Together, our simulations using alternative timing assumptions underscore the theoretical

benefit of delaying fiscal adjustment until after the economy has recovered from the worst

of the initial recession. However, the simulations strictly depend on the credibility of pre-

announced consolidation plans. If private agents harbor any doubts about the likelihood

of implementation, they will expect a less benign path for deficits and debt than has been

announced, and the sovereign risk premium will be correspondingly higher. In this sense,

the medium-term retrenchment scenario considered here may not actually be available as

a credible policy option, notably at times of significant concern about sovereign risk. This

notion is an important motivation for the present paper and explains the focus of most of

our analysis on fiscal adjustment scenarios that involve immediate spending cuts. That being

said, it bears repeating a key result of our earlier work in Corsetti et al. (2010): to the

extent that policymakers can credibly commit to future austerity, backloaded consolidation

strategies will generally garner superior outcomes in terms of near-term growth, as they avoid

tightening fiscal policy at a time when the central bank is unable to offset the contractionary

fiscal impulse.

36

4.3.2 Distortionary taxation

Distortionary taxes generally weigh on economic activity. To the extent that an early re-

trenchment reduces the need for distortionary taxation in the future, such a policy would

appear to be less harmful to growth than we have reported so far. Figure 8 assesses this

hypothesis, focusing again on results for three different levels of initial debt.25

Figure 8: Effects of retrenchment on output depending on taxation

Baseline Only labor taxes Labor tax after ZLB

a) Immediate retrenchment

0 5 10 15 20 25−2

0

2

4


0 5 10 15 20 25−2

0

2

4

0 5 10 15 20 25−2

0

2

4

b) Medium-term retrenchment

0 5 10 15 20 25

0

5

10

0 5 10 15 20 25

0

5

10

0 5 10 15 20 25

0

5

10

Notes: The panels show the effect of retrenchment on output for different assumptions about taxation. Theleft column reproduces the effect of retrenchment with lump-sum taxes (as in the baseline). The middle panelshows the effect of retrenchment when labor taxes are used throughout. The right column shows the effect ofretrenchment if taxes are lump-sum for the first 18 quarters but distortionary thereafter. For the simulationsin which labor taxes are used the initial shock has been rescaled such that for each debt level the severity ofthe recession and the length of the ZLB episode without retrenchment are roughly comparable to the baselineresponses shown in Figure 5.

The first column reproduces the responses for the baseline case, in which only lump-sum

25For this exercise, we fix the labor tax rate at 35 percent in the steady state, in line with the 2006 averageU.S. marginal income tax rate reported by Barro and Redlick (2011). Fluctuations in labor taxes ensure that(28) holds. For the scenarios with labor taxes, we set φT,bg = 0.0193 for all periods.

37

taxes are used. The second column shows how distortionary taxation alters the effect of

the spending cuts. In the simulations, distortionary taxes, if used throughout, have little

bearing on how fiscal retrenchment affects output. While lower future distortionary taxation

stimulates future economic activity, and thus current demand, a second, countervailing effect

is present. Without retrenchment, distortionary tax rates rise more strongly, with a view

toward stabilizing the rising debt burden. As stressed by Eggertsson (2011), to the extent

that higher labor tax rates raise inflation, they may help to stabilize output if the economy

is stuck at the ZLB. By contrast, an early retrenchment reduces the labor tax burden and

exerts a negative effect on activity. In the simulations shown here, this effect outweighs the

beneficial impact arising from the reduced tax burden in later periods.

One may argue, of course, about the likelihood that taxes would actually be raised while

the economy remains stuck at the ZLB. Since the timing of taxation is important for the

aforementioned finding, the rightmost column of Figure 8 shows the results for a different

taxation scenario. The goal is to disentangle the impact of fiscal retrenchment from the

specific effects that labor taxes have in a ZLB situation. Thus, the responses in the right

column are based on the assumption that lump-sum taxes are used for the first 18 quarters to

prevent debt from exploding. Only after these 18 quarters, and hence well after the end of the

ZLB episode, do labor taxes take over. For the 60 percent debt level, the difference relative to

the case of lump-sum taxation is small, and the effects are very similar to the baseline. For the

90 percent debt level, the output effects of retrenchment turn more favorable. However, this

mostly affects the medium-term retrenchment package. Finally, results for the highest debt

level shown here, i.e., 115 percent of debt to GDP, illustrate that the sovereign risk channel

may be stronger in the case with distortionary taxation, provided that changes in distortionary

tax rates materialize only after the ZLB has ceased to bind. Intuitively, for this level of

sovereign indebtedness, the heightened risk premium demands relatively strong increases in

distortionary taxes to finance the debt burden, which by itself worsens the recession. As a

result, an early retrenchment now crowds in output, and much more strongly so than in the

case with lump-sum taxes only.

38

4.3.3 Degree of monetary policy offset for risk premia

Next, we consider the sensitivity of our results with regard to the extent to which the central

bank is able to neutralize the effect of sovereign risk on private borrowing rates. Our baseline

simulations have assumed that once the economy has exited from the ZLB situation, the

central bank can set interest rates in a way that prevents sovereign risk from affecting economic

activity in any way.

Figure 9: Effects of retrenchment on output when CB cannot fully neutralize risk premia

Immediate Medium-term Persistent

Baseline – full neutralization

0 5 10 15 20 25

−2

−1

0

1


0 5 10 15 20 25

−2

0

2

0 5 10 15 20 25

−2

−1

0

1

2

Limited neutralization

0 5 10 15 20 25

−2

−1

0

1

0 5 10 15 20 25

−2

0

2

0 5 10 15 20 25

−2

−1

0

1

2

Notes: The figure shows the effect of the three retrenchment packages (described in the notes to Figure 7)for the case where the central bank does not fully offset the risk premium even once the economy has left theZLB. Top row shows the baseline responses for 60, 90, and 100 percent initial debt-to-GDP ratio. Bottomrow shows the case when the response coefficient φω is only 3/4 of the size of the benchmark calibration.

We now assess, instead, the effect of spending cuts if the central bank does not, or cannot, fully

neutralize the sovereign spread. In particular, we assume that the central bank’s response is

only three-quarters the size of the value of φω that we used in the previous simulations. To this

end, we set φω = 0.75(πb+sΩ). The first point to note about this scenario is that the baseline

39

recession is deeper, reflecting the stronger headwinds from persistently high risk premia. The

lower panels of Figure 9 show the effects of fiscal retrenchment relative to that new baseline.

By comparison, the upper panel revisits the baseline in which the central bank fully offsets

higher sovereign risk premia after the ZLB episode. As it turns out, early retrenchment is less

detrimental to economic activity at high initial debt levels in the lower panels. Intuitively,

the central bank’s limited willingness (or capacity) to neutralize higher spreads in the future

raises the benefit of fiscal retrenchment as a way to bring down long-term real interest rates

via the sovereign risk channel.

5 Conclusion

The present paper analyzes how the ”sovereign risk channel” affects macroeconomic dynamics

and stabilization policy. Through this channel, rising sovereign risk drives up private-sector

borrowing costs, unless higher risk premia are offset by looser monetary policy. If the central

bank is constrained in counteracting higher risk premia, sovereign risk becomes a critical

determinant of macroeconomic outcomes. Its implications for stabilization policy have not

been fully appreciated in earlier formal analyses, although they are likely to be of great

importance for many advanced economies currently facing intense fiscal strain.

Building on the model proposed by Curdia and Woodford (2009), we show that the sovereign

risk channel makes the economy (more) vulnerable to problems of indeterminacy. In partic-

ular, private-sector beliefs about a weakening economy can become self-fulfilling, driving up

risk premia and choking off demand. In this environment, a procyclical fiscal stance—that is,

tighter fiscal policy during economic downturns–can help to ensure determinacy.

Further, we find that sovereign risk tends to exacerbate the effects of negative cyclical shocks:

recessionary episodes will be deeper the stronger the sovereign risk channel, which in our

specification is a nonlinear function of public-sector indebtedness. Moreover, in deep reces-

sions that force the central bank down to the zero lower bound (ZLB) for nominal interest

rates, sovereign risk delays the exit from the ZLB, hence prolonging macroeconomic distress.

The sovereign risk channel also has a significant bearing on fiscal multipliers. Specifically,

the effect of government spending on aggregate output hinges on (i) the responsiveness of

private-sector risk premia to indicators of fiscal strain; and (ii) the length of time during

which monetary policy is expected to be constrained. Our analysis suggests that upfront

40

fiscal retrenchment is less detrimental to economic activity (i.e., multipliers are smaller) in the

presence of significant sovereign risk, as lower public deficits improve private-sector financing

conditions. In relatively extreme cases where fiscal strains are severe and monetary policy is

constrained for an extended period, fiscal tightening may even exert an expansionary effect.

That being said, fiscal retrenchment is no miracle cure. Indeed, all our simulations feature a

deep recession even if tighter fiscal policy, under the aforementioned conditions, may stimulate

economic activity relative to an even bleaker baseline.

As an additional caveat, we note that our analysis has focused on fiscal multipliers under

a go-it-alone policy that does not involve external financial support at below-market rates.

Availability of such support could allow countries to stretch out the necessary fiscal adjustment

as they benefit from lower funding costs and, possibly, positive credibility effects. Indeed,

if and where announcements of future fiscal adjustment are credible, delaying some of the

planned spending cuts remains a superior strategy in terms of protecting short-term growth.

How countries end up dealing with the challenges summarized here may prove to be a defining

feature of global economic developments over the coming years.

41

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45

A Three-equation representation of the aggregate economy

The following IS curve can be derived for the linearized model:

yt = yt+1 − (gt+1 − gt)−[Ξ(bt+1 − bt) + b (Ξt+1 − Ξt)

]

−σ[i dt − Πt+1 + Γt + (πb + sΩ)ωt − [ψΩ + sΩ(1− δ)]Ωt+1

],

where

Ωt = ωt + δ Ωt+1.

The New Keynesian Phillips curve reads as follows:

Πt = β Πt+1

+κ[(φ(1 + ν) + 1/σ − 1)yt − φ(1 + ν)zt − 1/σ[gt + Ξ bt + b Ξt]− τwt + [sΩ + πb − γb]Ωt

];

and the Taylor rule reads is given by:

i d,∗t = φΠΠt − φωωt.

idt = maxid,∗t ,−(1 + i d,∗)

.

This three-equation system, together with an assumption about the evolution of the spread

ωt, describes the dynamics of output, inflation, and interest rates (independently of private

debt) if

1. Ξ = 0, that is, no aggregate resource costs of loan origination.

2. [ψΩ + sΩ(1− δ)] = 0.

3. τwt = 0, that is, distortionary taxes do not move or are nonexistent.

4. [sΩ + πb − γb] = 0.

The parameters and laws of motion chosen in the paper satisfy these conditions.

B Linking ξ and ξ′

This appendix provides the foundation for equation (39) in the main text. The formula is

motivated through a sequence of back-of-the-envelope calculations. Focus on the interest rate

46

spread in the IS curve, neglecting other terms. Assume that initially, in period t, the economy

is at the ZLB. This gives a relationship of

yt = Etyt+1 − σ$t + ....

Iterating forward, we have

yt = −σEt

∞∑

j=0

$t+j I(economy at ZLB in period t+ j)

,

where I() is the indicator function. If the spread depends on the future debt level, as in the

full version of the model presented in Section 2, we have

$t+j = ξ′Et+j bgt+j+1,

so

yt = −σEt

∞∑

j=0

I(economy at ZLB in period t+ j) ξ′ Et+j bgt+j+1

.

Abstracting from the effect of interest payments and the valuation of debt, bgt+j+1 is roughly

the sum of initial debt in t− 1 (assumed to be zero without loss of generality in the following

exposition) and the deficits accumulated in period t through t + j + 1. Let deficit be the

primary deficit. Following the Markov structure, we assume that the primary deficit (before

extraordinary debt-stabilization measures) is the same in every period at the ZLB. With the

same abstraction as above, conditional on being at the ZLB in t+ j,

Et+j bgt+j+1 = bgt+j + µ · deficit = (j + 1 + µ) deficit.

Then,

yt = −σξ′Et

∞∑

j=0

I(economy at ZLB in period t+ j)(j + 1 + µ)deficit

.

And so

yt = −σ ξ′ deficit

∞∑

j=0

µj(j + 1 + µ),

or, equivalently.

yt = −σ ξ′1 + µ(1− µ)

(1− µ)2deficit. (43)

47

In contrast, the analytical version of the model in Section 3 has

yt = −σEt

∞∑

j=0

I(economy at ZLB in period t+ j)ξ deficit Et+j [ I(at ZLB in t+ j + 1)]

,

which boils down to

yt = −σ ξ∞∑

j=0

µj deficit µ.

Or, equivalently,

yt = −σ ξµ

1− µdeficit. (44)

Comparing (43) and (44) leads to the relationship in the main text, namely, equation (39):

ξ =1 + µ(1− µ)

µ(1− µ)ξ′.

C Proofs of propositions

C.1 Proof of Proposition 1

The economy, stripped from exogenous variables, is given by

Etzt+1 = Azt,

where zt = [yt; πt] and

A =1

aµβ

[µβ + σµκy −σµ

−aκy a

],

where a = (µ + µσξφT,y). The Blanchard-Kahn conditions for determinacy require that

matrix A have two roots outside the unit circle. Woodford (2003), pp. 670f., gives the

following necessary and sufficient conditions for determinacy:

either (Case I): (i) det(A) > 1, (ii) det(A) − tr(A) > −1, and (iii) det(A) + tr(A) > −1,

or (Case II): (i) det(A)− tr(A) < −1 and (ii) det(A) + tr(A) < −1.

In the current case, det(A) = 1aµβ and tr(A) = 1

aµβ [µβ + σµκy + a]. Since both det(A) > 0

and tr(A) > 0 Case II cannot be satisfied. Checking Case I, condition (iii) holds since both

terms are positive. Condition (i) of Case I is equivalent to condition a) in the proposition.

Condition (ii) of Case I is equivalent to condition b) in the proposition.

48


In this case

A =1

a∗µβ

[µβ + σ∗µκ∗y −σ∗µ

−a∗κ∗y a∗

],

where a∗, σ∗ and κ∗y are defined in the proposition.

1. Note that under the restriction that a∗ > 0, det(A) > 0. Therefore it cannot be the

case that det(A)− tr(A) < −1 and det(A) + tr(A) < −1. This means that determinacy

can only obtain under the conditions of Case I spelled out in the proof of Proposition 1.

Conditions (i) and (ii) of that case correspond to conditions a) and b) in Proposition 2.

In addition, if ϕ < 1 (as assumed), then tr(A) > 0, so det(A) + tr(A) > −1. Condition

(iii) of Case I is therefore obsolete.

2. For a∗ < 0, det(A) < 0, so Case I cannot hold. The conditions given in the proposition

are those pertaining to Case II.


The assumed Markov structure means that output, inflation, and government spending (in

deviations from the steady state) will take on the same respective values, yL, πL, and gL, in

every period in which monetary policy is constrained, and values of zero thereafter. The IS

curve thus implies

yL − gL = µ(yL − gL)− σ[− log(1 + id) + Γ + µξ(gL − φT,yyL)− µπL],

while the Phillips curve gives

πL = µβπL + κyyL − κggL.

Solving these equations for yL and πL yields:

yL = ϑr[log(1 + id)− Γ] + ϑggL,

where ϑr and ϑg take on the values given in the proposition. In addition, ϑr > 0: the numer-

ator is positive, and so is the denominator, per condition b) for determinacy in Proposition

1.

D Two corollaries

D.1 Statement and proof of Corollary 4

Corollary 4 Under the conditions of Proposition 2, the following special cases obtain:

1. With no endogenous risk premium (ξ = 0), the range of parameters for which the equi-

librium is determinate is larger if government spending is countercyclical (ϕ < 0), rather

49

than acyclical. In addition, the range of fundamental parameters implying determinacy

of the equilibrium is larger the more negative ϕ.

2. With an endogenous risk premium ξ > 0, instead, the range of parameters for which

the equilibrium is determinate is often larger if government spending is procyclical, that

is, if spending is cut systematically during a deep recession. More precisely: Under the

conditions of Proposition 2, if a∗ > 0, ϕ ∈ (0, 1), and φT,y < 1− κν(1−βµ)ξ , then the range

of fundamental parameters for which the equilibrium is determinate is at least as large

as in the absence of an endogenous spending response and can be larger. Note that this

case is more likely the less tax revenue responds to the state of the economy (the smaller

φT,y), and the more responsive the sovereign risk premium to the deficit (the larger ξ).

Proof.

1. If ξ = 0, a∗ = µ > 0. As a result, case 1 of Proposition 2 is the relevant one. First note

that condition a) will always be satisfied. What remains to be checked is condition b).

For the statement in the proposition, it suffices to observe that if ξ = 0 the left-hand

side of condition b) is independent of ϕ, and the right-hand side is strictly increasing

in ϕ.

2. In order for the range of fundamental parameters for which determinacy holds to be

bigger with ϕ ∈ (0, 1) under the stated conditions than with ϕ = 0, we have to have

a∗ < a, and

(1− βµ)(a− a∗) > µσ∗κ∗y − µσκy.

a∗ < a boils down toφT,y−ϕ

1−ϕ < φT,y, which is true for 0 < ϕ < 1.

The second condition reduces to

(1− βµ)ξ(1− φT,y)ϕ

1− ϕ> κν

ϕ

1− ϕ.

For ϕ ∈ (0, 1) this yields φT,y < 1− κν(1−βµ)ξ , the condition in the corollary.

D.2 Statement and proof of Corollary 5

Corollary 5 Under the conditions of Propositions 1 and 3:

1. The government spending multiplier, ϑg, is positive if and only if

(1− µ)−µσκg1− βµ

> µξσ. (45)

Note, conversely, that the spending multiplier can be negative if the risk premium has a

sufficiently detrimental effect on the economy, that is, if ξ is large enough.

50

2. Government spending at the lower bound is self-financing if ϑg > 1/φT,y. This is the

case if

φT,y >(1− βµ)(1− µ)− µσκy(1− βµ)(1 − µ)− µσκg

.

This cutoff is independent of ξ.

3. If ξ = 0, provided that the conditions for determinacy in Proposition 1 are satisfied, the

government spending multiplier is strictly larger than one. This case corresponds to the

analysis by Christiano et al. (2011) and Woodford (2011).

4. If ξ > 0, the government spending multiplier is unambiguously larger than 1 if φT,y >

1− κνξ(1−βµ) , that is, if tax revenue is sufficiently responsive to output.

Proof.

1. Under the restrictions for determinacy provided by Proposition 1, the denominator of

ϑg is unambiguously positive. ϑg > 0 thus requires (1 − βµ)(1 − b) − µσκg > 0, which

solves to the expression in equation (45).

2. The deficit (in deviation from the steady state) is given by gL − φT,yyL. Government

spending will thus be self-financing if 1 − φT,yϑg < 0. Insert the multiplier from equa-

tion (41), observe that the denominator is positive by the assumption of determinacy.

Substitute for a and b using the expressions given in the proposition. Simplifying yields

the desired inequality for φT,y.

3. The conditions for determinacy require that (1− βµ)(1− a)−µσκy > 0, so the denom-

inator of ϑg is positive. ϑg > 1 then boils down to

(1− βµ)(1− b)− µσκg > (1− βµ)(1− a)− µσκy.

Now, if ξ = 0 then a = b. ϑg > 1 therefore requires −µσκg > −µσκy, or κg < κy, which

is true.

4. For ξ > 0, ϑg > 1 is equivalent, after substituting κy − κy = κν, to φT,y > 1− κνξ(1−βµ) .

E Delayed fiscal retrenchment

The analytical results presented in Section 3 pertain to fiscal retrenchment while monetary

policy is constrained by the ZLB. For completeness, we also consider in this appendix a

retrenchment that is designed to take effect only once monetary policy has exited from the

ZLB. As discussed in Corsetti et al. (2010), fiscal consolidation generally reduces aggregate

51

demand and inflation when it occurs. However, the expectation of future fiscal consolidation

may unfold a positive upfront effect on output. Indeed, if spending cuts are implemented

when the central bank is no longer constrained, the policy rate will fall in both nominal and

real terms (recall, φπ > 1). In anticipation of the lower future path of short-term interest

rates, long-term interest rates decline immediately, boosting consumption and output.

By the nature of this transmission mechanism, the exact timing of consolidation is crucial.

When firms anticipate the future drop in demand, they start, because of nominal rigidities,

to reduce prices somewhat before the government cuts actually take place. In other words,

inflation eases in advance of the actual fiscal retrenchment. If much of the retrenchment is set

to occur too soon after the period in which monetary policy exits from the ZLB, the effect on

the real rate of interest can be perverse, that is, real rates may rise while monetary policy is

still constrained, hampering the recovery. In order to assess the effects on economic activity

more formally, we state the following proposition and corollary.

Proposition 6 In the economy specified in Proposition 1, let gt take on a value of 0 whenever

the interest rate is constrained to 0. In the first period in which this constraint on monetary

policy ceases to bind let gt = ga < 0, marking an episode of fiscal austerity. In each subsequent

period, let government spending remain at that austerity value with probability % ∈ [0, 1) and

otherwise return to gt = 0 forever. Assume that the conditions for determinacy are satisfied.

Then, while interest rates are constrained to zero, output is given by

yL = 1d

[σ(1− βµ)[log(1 + id)− Γ] + (1− µ)(1 − βµ)(1 + σξφT,y)(ya − ga) + σ(1− µ)πa

− (1− µ)(1 − βµ)σξ(1− φT,y)ga],

(46)

where d = (1−βµ)[1−a]− σµκy, a := µ+µξφT,yσ as in Proposition 1, and ya and πa denote,

respectively, output and inflation in the austerity period, equal to

ya =(1− %)(1 − β%) + σ(φπ − %)κg(1− %)(1− β%) + σ(φπ − %)κy

ga, (47)

and

πa =(1− %)(κy − κg)

(1− %)(1− β%) + σ(φπ − %)κyga. (48)

Proof. For the austerity phase the IS equation is given by

(ya − ga)(1− %) = −σ [φππa − %πa] ,

and the Phillips curve reads as

πa = β%πa + κyya − κgga.

52

These two equations solve to expressions (47) and (48).

At the ZLB, in turn, the IS equation is given by

yL(1− µ) = (1− µ)(ya − ga)

−σ[− log(1 + id) + Γ + ξ[(1 − µ)ga − φT,y(1− µ)ya − φT,yµyL]− µπL − (1− µ)πa

],

and the Phillips curve reads as

πL = βµπL + β(1− µ)πa + κyL.

Solving the latter two equations leads to the equation for output, yL, equation (46) in the

proposition.

Corollary 7 Under the conditions in Proposition 6,

1. if ξ = 0, retrenchment after monetary policy ceases to be constrained boosts economic

activity in the zero-interest rate phase unless too much of the retrenchment is expected

to occur too soon after the exit from the ZLB phase. More precisely, there exists a value

of % ∈ [0, 1) such that yL > 0 if ga < 0. This is the case for any % > 1+φπ(βµ−1)βµ .

2. Suppose that φT,y > 0 and that for the values of ξ considered here the equilibrium is

determinate. Suppose the fundamental parameters are such that the effect of future

austerity on yL would be positive without the sovereign risk channel (ξ = 0). Then the

magnitude of the effect of future retrenchment on yL will be larger still if the economy

is subject to the sovereign risk channel. Indeed, the effect will be larger, the larger ξ.

3. For some parameterization the effect of future austerity is positive if ξ > 0, while it is

negative if ξ = 0.

Proof.

1. For the case ξ = 0, abstracting from constants, we have that yL = 1/d[(1 − µ)(1 −

βµ)(ya − ga) + σ(1− µ)πa].

Note that d = (1 − µ)(1 − βµ) − σµκy > 0 since Proposition 6 assumes determinacy

of the equilibrium; cp. condition b) in Proposition 1. yL > 0 (meaning that future

austerity increases output at the ZLB relative to the case of no action) thus requires

(1− µ)(1− βµ)(ya − ga) + σ(1− µ)πa > 0. (49)

Substitute for ya and πa using equations (47) and (48). Further note that the denom-

inator in the expressions for πa and ya is positive (we have assumed determinacy in

Proposition 6, so φπ > 1, and therefore especially φπ − % > 0). Furthermore, observe

that κy − κg > 0, and that ga < 0. Using these observations, inequality (49) resolves to

% >1+φπ(βµ−1)

βµ .

53

2. Let superscript w denote outcomes at the ZLB with the sovereign risk channel in op-

eration (ξ > 0); ywL , for example, denotes output. With a superscript o, denote the

terms in the absence of the sovereign risk channel (ξ = 0). Note, first, that ya, ga, πaare independent of the interest spread. Note, second, that with ξ > 0 and φT,y > 0, we

have dw = (1 − βµ)(1 − µ − µξφT,yσ) − σµκy < do. Note, third, that dw > 0 by the

assumption of determinacy made in Proposition 6. Thus [ do

dw − 1] > 0.

We have to check

∂ywL/(−∂ga) > ∂yoL/(−∂ga) > 0. (50)

The first inequality, after substituting for ya and πa in (46), is equivalent to

[do

dw − 1]σ(1− µ)(κg − κy) [(1− βµ)(φπ − %)− 1 + %]

+ do

dw σ(φπ − %)(κg − κy)σξφT,y(1− µ)(1− βµ)

+ do

dw (1− µ)(1− βµ) [(1− %)(1− β%) + σ(φπ − %)κy] σξ(φT,y − 1) < 0.

The second row is strictly negative because φπ > 1 > % and κg < κy. The third row

is strictly negative since φT,y ∈ (0, 1). As for the first row, since κg − κy < 0 it will

be strictly negative if (1 − βµ)(φπ − %) − 1 + % > 0. This condition is equivalent to

the condition for a positive effect of future retrenchment with ξ = 0 stated in item 1

of the corollary, namely % > 1+φπ(βµ−1)βµ . Therefore, whenever the second inequality in

(50) holds, so does the first.

3. It suffices to show one such parameterization. In particular, let φT,y = 0. In that case,

the sovereign risk channel does not affect the determinacy condition, nor does it affect

the denominator defined as d above. The condition that ensures that a retrenchment

after the ZLB has a positive effect on output at the ZLB is

1

d[(1− µ)(1− βµ)(ya − ga) + σ(1− µ)πa − (1− µ)(1− βµ)σξga] > 0

Now, ya, πa do not depend on ξ. In addition, under the conditions provided in the

proposition, (1− µ)(1− βµ)σξ is unambiguously positive if ξ > 0, while ga is negative.

As a result, for any persistence of the retrenchment % (and so in particular also for

those that violate the inequality provided in item 1 of the corollary), there exist values

of ξ > 0 that make the above condition hold.

Here we are primarily interested in the output effects during the period in which monetary

policy is constrained. Corollary 7 provides a detailed characterization. In the absence of a

sovereign risk channel, the corollary shows that future spending cuts that take effect after the

end of the ZLB phase raise output in the early periods unless too much of the retrenchment is

expected to occur soon after the exit from the ZLB, i.e., future retrenchment efforts need to

be sufficiently persistent; compare Corsetti et al. (2010) and Woodford (2011). The corollary

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also highlights that the sovereign risk channel would enhance any crowding-in of output while

at the ZLB; see Item 2 of Corollary 7. In addition, for certain parameterizations, future

retrenchment, even if not particularly persistent, may stimulate output at the ZLB if the

fiscal situation is fragile (ξ > 0), whereas such a retrenchment would have negative effects in

the absence of the sovereign risk channel, that is, for ξ = 0 (Item 3).

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Sovereign Risk, Fiscal Policy, and Macroeconomic …Sovereign Risk, Fiscal Policy, and Macroeconomic Stability Prepared by Giancarlo Corsetti, Keith Kuester, Andre Meier, and Gernot